pacman::p_load(olsrr, ggstatsplot, sf, tmap, tidyverse, gtsummary, performance, see, sfdep, spdep, tidygeocoder)TH3: Prototyping Modules for Geospatial Analytics Shiny Application
Take Home Exercise 3
TH3.1 Introduction
The objective of Take-Home Exercise 3 is to prototype a module to be built for the Geospatial Analytics project, which will serve to analyse housing prices in Johor Bahru.
Since separating from Malaysia in 1965, Singapore has seen a rapid development in its economy and quality of life the likes of which no one else has seen. So it made sense for the neighbouring city of Johor Bahru, Malaysia, to capitalise on the spillover effects of Singapore’s prosperity by itself becoming a lifestyle hub for visiting Singaporeans, and an emerging business satellite for companies from Singapore and the region. New malls have sprouted all over the state capital, and new investments were made by the state and federal governments to boost the city’s economy, such as the development areas of Iskandar Puteri and Pasir Gudang, the Johor Bahru-Singapore rapid transit link and the Iskandar Puteri stop on the since-shelved Kuala Lumpur-Singapore High Speed Rail, among many others. In particular, Johor Bahru became a place where Singaporeans could buy houses at prices cheaper than in their hometown - even more so when housing prices in the country began to fly through the roof in recent times. Even while this phenomenon led to further economic growth, there were concerns that the presence of these Singaporean buyers would put inflationary pressure on the city.
Admist all this, this project aims to explore the trajectory and factors influencing housing prices in Johor Bahru. Using the measures of local and global spatial autocorrelation and a hedonic pricing model, we will perform geospatial data analysis on property transaction data in Johor Bahru and its northwestern neighbour Kulai. As the group member in charge of exploratory data analysis, this take-home exercise serves to prototype the module for performing hot and cold spot analysis.
The scope of today’s exercise will be as follows:
- Load and clean the geospatial and aspatial data required for the analysis
- Geocode the aspatial property transaction data
- Create a hexagonal grid of the study area prior to performing analysis
- Perform exploratory data analysis
- Derive the local measures of spatial autocorrelation, and perform hot/cold spot analysis
- Prototype the UI for the corresponding part of the project
TH3.2 Loading data
Today’s exercise will involve going through the entire data acquisition process from start to finish. This includes sourcing and cleaning the data before it is used for analysis.
TH3.2.1 Loading geospatial data
We will be using Malaysia’s municipality polygons, sourced from the United Nations Humanitarian Data Exchange.
adm3_my <- st_read(dsn = 'shiny/data/geospatial/myadm3', layer = 'geoBoundaries-MYS-ADM3') %>%
st_transform(3377)Reading layer `geoBoundaries-MYS-ADM3' from data source
`/Users/kendricktty/Gits/smu_cs/is415-site/TakeHome/TakeHome3/shiny/data/geospatial/myadm3'
using driver `ESRI Shapefile'
Simple feature collection with 1859 features and 5 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 98.93646 ymin: 0.8538234 xmax: 115.6782 ymax: 6.726112
Geodetic CRS: WGS 84qtm(adm3_my)
The overall shape of the plot is as above, corresponding to the geography of Peninsula (West) Malaysia, as well as the eastern states of Sabah and Sarawak.
TH3.2.2 Loading property transaction data
property_transaction_data <- read_csv('shiny/data/aspatial/Open Transaction Data.csv')New names:
Rows: 20517 Columns: 14
── Column specification
──────────────────────────────────────────────────────── Delimiter: "," chr
(12): Property Type, District, Mukim, Scheme Name/Area, Road Name, Month... num
(1): Land/Parcel Area lgl (1): ...14
ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
Specify the column types or set `show_col_types = FALSE` to quiet this message.
• `Unit` -> `Unit...9`
• `Unit` -> `Unit...11`
• `` -> `...14`head(property_transaction_data)# A tibble: 6 × 14
`Property Type` District Mukim `Scheme Name/Area` `Road Name`
<chr> <chr> <chr> <chr> <chr>
1 1 - 1 1/2 Storey Semi-Detached Johor Bah… Band… KAW ABDUL SAMAD/M… JLN ISMAIL
2 1 - 1 1/2 Storey Semi-Detached Johor Bah… Band… KAW ABDUL SAMAD/M… JLN ABDUL …
3 1 - 1 1/2 Storey Semi-Detached Johor Bah… Band… KAW ABDUL SAMAD/M… JLN YUSOF …
4 1 - 1 1/2 Storey Semi-Detached Johor Bah… Band… KIM TENG PARK JLN BERLIAN
5 1 - 1 1/2 Storey Semi-Detached Johor Bah… Band… KIM TENG PARK JLN UNGKU …
6 1 - 1 1/2 Storey Semi-Detached Johor Bah… Band… LARKIN GARDEN JLN DATO J…
# ℹ 9 more variables: `Month, Year of Transaction Date` <chr>, Tenure <chr>,
# `Land/Parcel Area` <dbl>, Unit...9 <chr>, `Main Floor Area` <chr>,
# Unit...11 <chr>, `Unit Level` <chr>, `Transaction Price` <chr>, ...14 <lgl>TH3.3 Data Preprocessing
TH3.3.1 Filtering Mukims outside Johor Bahru
We are only concerned with Mukims within Johor Bahru and Kulai district - the latter of which contains Johor Bahru’s main Senai international airport. Hence, we will need to filter these out.
johor_kulai_mukims <- c("MUKIM JELUTONG", "MUKIM PLENTONG", "MUKIM PULAI", "MUKIM SUNGAI TIRAM", "MUKIM TANJUNG KUPANG", "MUKIM TEBRAU", "BANDAR JOHOR BAHRU", "MUKIM BUKIT BATU", "MUKIM KULAI", "BANDAR KULAI", "MUKIM SEDENAK", "MUKIM SENAI")
adm3_jb_kulai <- adm3_my %>%
filter(shapeName %in% johor_kulai_mukims)
tmap_mode('view')tmap mode set to interactive viewingtm_shape(adm3_jb_kulai) +
tm_polygons()As we can see, there are still some stray polygons located very far north from Johor Bahru and Kulai proper that we have to remove. A quick inspection of the dataframe in memory indicates they are associated with the Mukims of Pulai and Jelutong, and carry the IDs 4, 5, 6, 16.
The code chunk below will break up the multipolygons into simple polygons, and remove the strays. The result is the correct, contiguous borders of the Mukims in Johor Bahru and Kulai districts.
broken_up_jb <- adm3_jb_kulai %>%
st_cast("POLYGON")Warning in st_cast.sf(., "POLYGON"): repeating attributes for all
sub-geometries for which they may not be constantstray_polygons <- c(4, 5, 6, 16)
adm3_jb_kulai <- broken_up_jb %>%
filter(!row_number() %in% stray_polygons)
tm_shape(adm3_jb_kulai) +
tm_polygons() +
tm_basemap("OpenStreetMap")write_rds(adm3_jb_kulai, 'shiny/data/rds/adm3_jb_kulai.rds')TH3.3.2 Geocoding Property Data
The raw dataset encodes information about street names, but we need latitudes and longitudes to plot their locations on a map. Therefore, it would be necessary to geocode the data. A dataset as large as ours took at least 2 hours to geocode, so it would be useful to save it as an RDS for later.
property_transaction_sf <- property_transaction_data %>%
mutate(Address = if_else(
!is.na(`Road Name`),
paste(`Road Name`, District, sep = " "), # Concatenate "Road Name" and "District" if "Road Name" is not NA
paste(`Scheme Name/Area`, District, sep = " ") # Else, concatenate "Scheme Name/Area" and "District"
)) %>%
geocode(address = Address, method = "osm", lat = "latitude", long = "longitude")
write_rds(property_transaction_sf, "shiny/data/rds/property_transaction_sf.rds")I learned the hard way to encode all longitudes and latitudes with WGS 84 first before transforming it into my desired coordinate system.
property <- read_rds("shiny/data/rds/property_transaction_sf_notnull.rds") %>%
st_as_sf(coords = c("longitude", "latitude"), crs = 4326) %>% st_transform(3377)TH3.3.3 Final Preprocessing
Finally, to make our dataset compatible for machine learning use, we need to encode two categorical variables we want to ingest: the Property Type and tenure.
Since Property Type is multiclass categorical, we need to perform one-hot encoding. The following code chunk performs one-hot encoding on the Property Type feature.
dummies <- model.matrix(~ `Property Type` - 1, data = property) %>% as.data.frame()
colnames(dummies) <- gsub("Property Type", "", colnames(dummies))
property <- property %>%
bind_cols(dummies) %>%
select(-`Property Type`)Since Tenure is binary categorical (the property is either freehold or leasehold), we can perform binary encoding on this feature.
property <- property %>%
mutate(is_leasehold = ifelse(Tenure == "Leasehold", 1, 0)) %>%
select(-Tenure)Finally, to help us join the property data with our polygon data later, we need to modify the “Mukim” column in the property data column to match that in the polygon data column.
property <- property %>%
mutate(Mukim = if_else(
!startsWith(Mukim, "Bandar"),
paste("Mukim", Mukim),
Mukim
)) %>%
mutate(Mukim = toupper(Mukim))We also need to parse the number in the Transaction Price column and convert the price from Malaysian Ringgit to US dollars.
property <- property %>%
mutate(
`Transaction Price` = parse_number(`Transaction Price`),
`Transaction Price` = `Transaction Price` * 0.21
)The last step is to remove the columns we will not need.
property <- property %>%
select(-`District`, -`Road Name`, -`Month, Year of Transaction Date`, -`Unit...9`, -`Unit...11`, -`Unit Level`, -`Address`, -`...14`)
write_rds(property, "shiny/data/rds/property_preprocessed.rds")To visualise the results, we can now plot our work onto a map.
tmap_mode('view')tmap mode set to interactive viewingtm_shape(adm3_jb_kulai)+
tm_borders() +
tm_shape(property) +
tm_dots(col = "Transaction Price",
alpha = 0.6,
style="kmeans",
n = 10) +
tm_view(set.zoom.limits = c(11,14)) +
tm_basemap('OpenStreetMap')TH3.4 Preparing for hot/cold spot analysis
TH3.4.1 Creating spatial grids
Johor Bahru is a relatively less dense location than Singapore to its south, so directly performing hot/cold spot analysis on its smaller number of Mukims would not make much sense. Instead, we will create a spatial grid subdividing the area into hexagons of equal diameter, and count the price of property sales located within each zone. The result is a hexagonal grid spanning the districts of Johor Bahru and Kulai, as shown below.
tmap_mode('plot')tmap mode set to plottingjb_kulai_hex <- st_make_grid(adm3_jb_kulai, cellsize = c(750, 750), what = "polygons", square = FALSE) %>%
st_sf() %>%
mutate(index = as.factor(row_number()))
jb_kulai_border <- adm3_jb_kulai %>% st_union()
jb_kulai_grid <- st_intersection(jb_kulai_hex, jb_kulai_border)Warning: attribute variables are assumed to be spatially constant throughout
all geometries# Check if hex grid intersects any polygons using st_intersects
# Returns a list of intersecting hexagons
intersection_list = jb_kulai_hex$index[lengths(st_intersects(jb_kulai_hex, jb_kulai_grid)) > 0]
# Filter for the intersecting hexagons
jb_kulai_grid = jb_kulai_hex %>%
filter(index %in% intersection_list)
tm_shape(jb_kulai_grid) +
tm_polygons(alpha = 0.2)
joined <- st_join(jb_kulai_hex, adm3_jb_kulai, join = st_intersects, left = FALSE)
aggregated <- joined %>%
group_by(index) %>%
summarise(`Mukim` = first(`shapeName`))
jb_kulai_grid$Mukim <- aggregated$Mukim
jb_kulai_grid <- jb_kulai_grid %>%
mutate(index = as.factor(row_number()))
jb_kulai_grid <- jb_kulai_grid[, c("Mukim", setdiff(names(jb_kulai_grid), "Mukim"))]
tmap_mode('view')tmap mode set to interactive viewingtm_shape(jb_kulai_grid) +
tm_fill(col = "Mukim",
alpha = 0.7)+
tm_basemap("OpenStreetMap")TH3.4.2 Exploratory Data Analysis
With our hexagonal grid, we can now perform exploratory data analysis. Using st_intersects allows us to map each point to a cell in the hexagonal grid.
intersections <- st_intersects(jb_kulai_grid, property)
jb_kulai_grid$density <- lengths(intersections)
tmap_mode('plot')tmap mode set to plottingtm_shape(jb_kulai_grid) +
tm_fill(col = "density",
palette = "Purples",
style = "quantile",
n = 10,
title = "Property density"
) +
tm_borders(col = "grey") +
tm_legend(position = c("RIGHT", "BOTTOM"))
The following code chunk allows us to aggregate the average, median and maximum property prices within each hexagonal cell.
# Extract average and maximum property price for each cell
aggregate_price <- function(i, method = "median") {
if (length(i) == 0 || all(is.na(property$`Transaction Price`[i]))) return(0)
if (method == "mean") {
return(mean(property$`Transaction Price`[i], na.rm = TRUE))
} else if (method == "max") {
return(mean(property$`Transaction Price`[i], na.rm = TRUE))
} else if (method == "median") {
return(median(property$`Transaction Price`[i], na.rm = TRUE))
} else {
stop("Invalid method: Choose either 'mean' or 'max'.")
}
}
avg_prices <- sapply(intersections, aggregate_price, method = "mean")
jb_kulai_grid$avg_price <- avg_prices
median_prices <- sapply(intersections, aggregate_price, method = "median")
jb_kulai_grid$median_price <- median_prices
max_prices <- sapply(intersections, aggregate_price, method = "max")
jb_kulai_grid$max_price <- max_prices
write_rds(jb_kulai_grid, "shiny/data/rds/jb_kulai_grid.rds")With these values calculated, we can plot them, along with our hexagonal grid, onto a map.
medians_map <- tm_shape(jb_kulai_grid) +
tm_fill(col = "median_price",
palette = "YlGn",
style = "kmeans",
n = 10,
title = "Median Property Price"
) +
tm_borders(col = "grey") +
tm_legend(position = c("RIGHT", "BOTTOM"))
averages_map <- tm_shape(jb_kulai_grid) +
tm_fill(col = "avg_price",
palette = "Purples",
style = "kmeans",
n = 10,
title = "Average Property Price"
) +
tm_borders(col = "grey") +
tm_legend(position = c("RIGHT", "BOTTOM"))
maximums_map <- tm_shape(jb_kulai_grid) +
tm_fill(col = "max_price",
palette = "YlOrRd",
style = "kmeans",
n = 10,
title = "Median Property Price"
) +
tm_borders(col = "grey") +
tm_legend(position = c("RIGHT", "BOTTOM"))
tmap_arrange(medians_map, averages_map, maximums_map, ncol = 3)Some legend labels were too wide. These labels have been resized to 0.47, 0.47, 0.44, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41. Increase legend.width (argument of tm_layout) to make the legend wider and therefore the labels larger.
Some legend labels were too wide. These labels have been resized to 0.47, 0.47, 0.44, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41. Increase legend.width (argument of tm_layout) to make the legend wider and therefore the labels larger.
Some legend labels were too wide. These labels have been resized to 0.47, 0.47, 0.44, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41. Increase legend.width (argument of tm_layout) to make the legend wider and therefore the labels larger.
# Plot the medians onto an interactive OpenStreetMap
tmap_mode('view')tmap mode set to interactive viewingmedians_map +
tm_basemap('OpenStreetMap')legend.postion is used for plot mode. Use view.legend.position in tm_view to set the legend position in view mode.tmap_mode('plot')tmap mode set to plottingThe highest median property prices in the study area appear clustered towards the centre of town (Bandar Johor Bahru), or towards Iskandar Puteri (within Pulai) towards the West. Notice their proximity to the two land border crossings with Singapore: the JB Sentral-Woodlands crossing (the causeway) connects with Bandar Johor Bahru, while the Tanjung Kupang-Tuas crossing (the second link) is towards the west - near Pulai. Pasir Gudang to the east (within Plentong) is the most recent area in Johor Bahru to be prominently industrialised, but the residential properties there do not fetch nearly as high a price - indicating a relative lack of demand.
As for Kulai, areas with higher property prices appear clustered towards Bandar Kulai, or Senai - the location of Johor’s international airport and a major industrial hub.
TH3.5 Computing Local Moran’s I
With exploratory data analysis complete, we can proceed to compute the measures of local spatial autocorrelation. We will first derive the local Moran’s I values for the median property price values with the following code chunk.
# Compute queen contiguity weights - no need to account for islands
wm_q <- poly2nb(jb_kulai_grid, queen=TRUE)
rswm_q <- nb2listw(wm_q, style = "W", zero.policy = TRUE)
# Compute local Moran's I
fips <- order(jb_kulai_grid$index)
localMI <- localmoran(jb_kulai_grid$median_price, rswm_q)
printCoefmat(data.frame(
localMI[fips,],
row.names=jb_kulai_grid$index[fips]),
check.names = FALSE
) Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
1 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
2 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
3 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
4 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
5 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
6 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
7 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
8 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
9 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
10 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
11 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
12 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
13 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
14 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
15 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
16 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
17 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
18 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
19 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
20 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
21 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
22 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
23 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
24 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
25 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
26 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
27 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
28 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
29 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
30 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
31 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
32 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
33 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
34 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
35 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
36 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
37 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
38 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
39 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
40 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
41 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
42 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
43 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
44 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
45 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
46 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
47 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
48 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
49 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
50 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
51 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
52 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
53 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
54 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
55 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
56 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
57 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
58 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
59 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
60 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
61 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
62 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
63 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
64 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
65 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
66 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
67 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
68 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
69 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
70 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
71 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
72 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
73 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
74 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
75 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
76 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
77 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
78 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
79 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
80 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
81 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
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1023 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
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1848 -1.3819e-01 -4.5915e-05 3.0937e-02 -7.8541e-01 0.4322
1849 6.0565e-01 -1.4880e-03 1.0012e+00 6.0678e-01 0.5440
1850 6.4207e-02 -4.5915e-05 3.0937e-02 3.6530e-01 0.7149
1851 6.4786e+00 -3.2731e-03 2.1983e+00 4.3718e+00 0.0000
1852 1.0165e+01 -3.7467e-03 2.5152e+00 6.4121e+00 0.0000
1853 4.0626e+00 -1.2685e-03 8.5364e-01 4.3984e+00 0.0000
1854 1.1240e+00 -1.2890e-04 8.6849e-02 3.8144e+00 0.0001
1855 1.6195e+00 -3.1515e-04 2.1229e-01 3.5157e+00 0.0004
1856 9.8833e-01 -1.4771e-04 9.9515e-02 3.1334e+00 0.0017
1857 4.6373e+00 -2.1666e-03 1.4567e+00 3.8439e+00 0.0001
1858 2.9398e+00 -1.2685e-03 8.5364e-01 3.1832e+00 0.0015
1859 6.1643e-01 -6.4944e-04 4.3733e-01 9.3311e-01 0.3508
1860 2.7407e-02 -4.5915e-05 3.0937e-02 1.5608e-01 0.8760
1861 -4.3268e-02 -4.5915e-05 3.0937e-02 -2.4573e-01 0.8059
1862 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1863 3.6546e-02 -4.5915e-05 3.0937e-02 2.0804e-01 0.8352
1864 3.1333e-02 -1.5120e-05 1.0188e-02 3.1057e-01 0.7561
1865 3.4667e-01 -5.3290e-04 3.5889e-01 5.7956e-01 0.5622
1866 8.9381e-02 -8.0176e-05 5.4021e-02 3.8490e-01 0.7003
1867 1.7659e-02 -4.5915e-05 3.0937e-02 1.0066e-01 0.9198
1868 1.1762e+00 -1.9655e-04 1.3242e-01 3.2327e+00 0.0012
1869 2.6383e+00 -3.7450e-04 2.5226e-01 5.2536e+00 0.0000
1870 8.3762e-01 -2.4397e-04 1.6435e-01 2.0667e+00 0.0388
1871 5.3181e-02 -2.6091e-04 1.7576e-01 1.2747e-01 0.8986
1872 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1873 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1874 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1875 8.8334e-02 -4.5915e-05 3.0937e-02 5.0247e-01 0.6153
1876 -7.7875e-02 -4.5915e-05 3.0937e-02 -4.4248e-01 0.6581
1877 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1878 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1879 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1880 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1881 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
1882 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1883 -3.8702e-01 -4.5915e-05 3.0937e-02 -2.2001e+00 0.0278
1884 6.2613e+00 -2.3567e-03 1.5843e+00 4.9763e+00 0.0000
1885 -5.7647e-02 -4.5915e-05 3.0937e-02 -3.2748e-01 0.7433
1886 -1.9205e-01 -4.5915e-05 3.0937e-02 -1.0916e+00 0.2750
1887 6.2798e-02 -3.9330e-04 2.6492e-01 1.2277e-01 0.9023
1888 -1.0663e-01 -4.5915e-05 3.0937e-02 -6.0598e-01 0.5445
1889 1.2016e+01 -4.1143e-03 2.7610e+00 7.2340e+00 0.0000
1890 4.7593e+00 -1.4819e-03 9.9704e-01 4.7678e+00 0.0000
1891 3.0864e+00 -7.7750e-04 5.2350e-01 4.2668e+00 0.0000
1892 1.5373e+00 -3.3436e-04 2.2523e-01 3.2400e+00 0.0012
1893 1.2674e+00 -3.5415e-04 2.3855e-01 2.5957e+00 0.0094
1894 2.0886e+00 -5.6665e-04 3.8161e-01 3.3819e+00 0.0007
1895 3.6104e+00 -7.7750e-04 5.2350e-01 4.9910e+00 0.0000
1896 1.0693e+00 -1.1708e-04 7.8884e-02 3.8074e+00 0.0001
1897 -2.3214e-01 -4.5915e-05 3.0937e-02 -1.3195e+00 0.1870
1898 -1.3710e-01 -4.5915e-05 3.0937e-02 -7.7918e-01 0.4359
1899 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1900 1.0966e-01 -4.5915e-05 3.0937e-02 6.2371e-01 0.5328
1901 1.0498e-01 -8.5022e-05 5.7286e-02 4.3895e-01 0.6607
1902 8.3539e-01 -2.1179e-04 1.4268e-01 2.2122e+00 0.0270
1903 2.3891e-01 -1.8189e-04 1.2254e-01 6.8301e-01 0.4946
1904 3.3500e-02 -4.5915e-05 3.0937e-02 1.9072e-01 0.8487
1905 9.0771e-02 -4.5915e-05 3.0937e-02 5.1633e-01 0.6056
1906 5.0277e+00 -8.7367e-03 5.8356e+00 2.0849e+00 0.0371
1907 1.5612e+00 -3.2468e-04 2.1871e-01 3.3390e+00 0.0008
1908 8.7412e-01 -2.1179e-04 1.4268e-01 2.3147e+00 0.0206
1909 -2.9621e-02 -4.5915e-05 3.0937e-02 -1.6814e-01 0.8665
1910 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1911 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1912 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1913 6.5187e-02 -2.1179e-04 1.4268e-01 1.7314e-01 0.8625
1914 1.9608e-02 -4.5915e-05 3.0937e-02 1.1174e-01 0.9110
1915 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1916 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1917 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1918 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
1919 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
1920 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1921 2.9740e+00 -5.1698e-03 3.4656e+00 1.6003e+00 0.1095
1922 -3.1049e-01 -4.5915e-05 3.0937e-02 -1.7650e+00 0.0776
1923 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1924 -1.4307e-01 -4.5915e-05 3.0937e-02 -8.1312e-01 0.4161
1925 6.4207e-02 -4.5915e-05 3.0937e-02 3.6530e-01 0.7149
1926 -7.0250e-01 -4.5915e-05 3.0937e-02 -3.9937e+00 0.0001
1927 8.1389e+00 -1.6118e-03 1.0844e+00 7.8175e+00 0.0000
1928 4.1473e+00 -1.1033e-03 7.4262e-01 4.8139e+00 0.0000
1929 2.1725e+00 -5.5780e-04 3.7566e-01 3.5455e+00 0.0004
1930 1.8963e+00 -6.6310e-04 4.4652e-01 2.8389e+00 0.0045
1931 6.3163e-01 -1.1708e-04 7.8884e-02 2.2493e+00 0.0245
1932 2.2663e+00 -4.3897e-04 2.9566e-01 4.1688e+00 0.0000
1933 3.1178e+00 -9.2516e-04 6.2283e-01 3.9518e+00 0.0001
1934 9.3012e-01 -2.6959e-04 1.8161e-01 2.1832e+00 0.0290
1935 -1.4319e-01 -4.5915e-05 3.0937e-02 -8.1382e-01 0.4158
1936 -3.9613e-02 -4.5915e-05 3.0937e-02 -2.2495e-01 0.8220
1937 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1938 -6.4883e-02 -9.7758e-05 6.5866e-02 -2.5243e-01 0.8007
1939 4.0650e-01 -7.2265e-05 4.8691e-02 1.8425e+00 0.0654
1940 9.8378e-01 -2.1179e-04 1.4268e-01 2.6050e+00 0.0092
1941 2.1314e-02 -4.5915e-05 3.0937e-02 1.2144e-01 0.9033
1942 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1943 -3.6740e-01 -4.5915e-05 3.0937e-02 -2.0885e+00 0.0367
1944 4.7551e+00 -8.6299e-04 5.8101e-01 6.2395e+00 0.0000
1945 1.3956e+00 -4.9305e-04 3.3207e-01 2.4227e+00 0.0154
1946 4.0913e-01 -3.0389e-04 2.0471e-01 9.0493e-01 0.3655
1947 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1948 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1949 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1950 3.8374e-02 -4.5915e-05 3.0937e-02 2.1843e-01 0.8271
1951 -1.6757e-01 -8.7556e-04 5.8947e-01 -2.1712e-01 0.8281
1952 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1953 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1954 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1955 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
1956 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
1957 -2.4569e-01 -4.5915e-05 3.7134e-02 -1.2747e+00 0.2024
1958 -4.2662e-01 -4.5915e-05 3.0937e-02 -2.4252e+00 0.0153
1959 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1960 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1961 -3.7179e-01 -4.5915e-05 3.0937e-02 -2.1135e+00 0.0346
1962 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1963 5.2624e+00 -2.7750e-03 1.8647e+00 3.8558e+00 0.0001
1964 3.0299e+00 -3.9542e-04 2.6634e-01 5.8718e+00 0.0000
1965 3.7841e+00 -1.1390e-03 7.6662e-01 4.3232e+00 0.0000
1966 2.0703e+00 -5.0856e-04 3.4251e-01 3.5384e+00 0.0004
1967 7.6959e-01 -1.1708e-04 7.8884e-02 2.7405e+00 0.0061
1968 9.7452e-01 -1.3752e-04 9.2653e-02 3.2020e+00 0.0014
1969 2.8453e+00 -9.3329e-04 6.2829e-01 3.5907e+00 0.0003
1970 1.7331e+00 -5.2676e-04 3.5476e-01 2.9106e+00 0.0036
1971 2.3857e-01 -2.5237e-04 1.7001e-01 5.7920e-01 0.5625
1972 -1.1668e+00 -1.8103e-03 1.2176e+00 -1.0557e+00 0.2911
1973 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1974 1.0966e-01 -4.5915e-05 3.0937e-02 6.2371e-01 0.5328
1975 1.2510e-01 -6.6492e-05 4.4802e-02 5.9132e-01 0.5543
1976 1.0749e+00 -1.7518e-03 1.1783e+00 9.9181e-01 0.3213
1977 -9.9321e-02 -4.5915e-05 3.0937e-02 -5.6441e-01 0.5725
1978 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1979 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1980 -8.7333e-01 -4.5915e-05 3.0937e-02 -4.9650e+00 0.0000
1981 2.6678e+00 -7.4804e-04 5.0368e-01 3.7601e+00 0.0002
1982 5.5770e-01 -5.9622e-04 4.0151e-01 8.8107e-01 0.3783
1983 7.5173e-02 -4.5915e-05 3.0937e-02 4.2765e-01 0.6689
1984 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1985 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1986 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1987 4.7753e-02 -1.7265e-05 1.1633e-02 4.4290e-01 0.6578
1988 1.9608e-02 -4.5915e-05 3.0937e-02 1.1174e-01 0.9110
1989 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1990 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1991 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
1992 1.8582e-01 -4.5915e-05 9.2904e-02 6.0978e-01 0.5420
1993 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
1994 -3.5357e-01 -4.5915e-05 4.6429e-02 -1.6407e+00 0.1009
1995 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
1996 1.1270e-01 -4.5915e-05 3.0937e-02 6.4103e-01 0.5215
1997 -3.9153e-01 -4.5915e-05 3.0937e-02 -2.2257e+00 0.0260
1998 -2.5018e-01 -4.5915e-05 3.0937e-02 -1.4221e+00 0.1550
1999 -8.5917e-02 -4.5915e-05 3.0937e-02 -4.8821e-01 0.6254
2000 5.1735e+00 -4.1143e-03 2.7610e+00 3.1160e+00 0.0018
2001 3.1680e+00 -8.6926e-04 5.8523e-01 4.1423e+00 0.0000
2002 1.9406e+00 -5.0856e-04 3.4251e-01 3.3167e+00 0.0009
2003 1.7502e+00 -4.3897e-04 2.9566e-01 3.2195e+00 0.0013
2004 8.1981e-01 -8.5022e-05 5.7286e-02 3.4256e+00 0.0006
2005 1.8638e+00 -3.9436e-04 2.6563e-01 3.6171e+00 0.0003
2006 2.1038e+00 -5.8327e-04 3.9280e-01 3.3577e+00 0.0008
2007 1.0559e+00 -2.4397e-04 1.6435e-01 2.6051e+00 0.0092
2008 -2.2239e-01 -4.5915e-05 3.0937e-02 -1.2641e+00 0.2062
2009 -3.9613e-02 -4.5915e-05 3.0937e-02 -2.2495e-01 0.8220
2010 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2011 -2.9255e-02 -4.5915e-05 3.0937e-02 -1.6606e-01 0.8681
2012 -2.4518e-01 -4.5915e-05 3.0937e-02 -1.3937e+00 0.1634
2013 4.2333e-01 -1.9655e-04 1.3242e-01 1.1639e+00 0.2445
2014 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2015 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2016 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2017 1.7696e+00 -7.8437e-03 5.2439e+00 7.7618e-01 0.4376
2018 -2.4518e-01 -4.5915e-05 3.0937e-02 -1.3937e+00 0.1634
2019 -6.7395e-02 -4.5915e-05 3.0937e-02 -3.8291e-01 0.7018
2020 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2021 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2022 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2023 1.3586e-01 -4.5915e-05 3.0937e-02 7.7265e-01 0.4397
2024 -3.0352e-02 -4.5915e-05 3.0937e-02 -1.7230e-01 0.8632
2025 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2026 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2027 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
2028 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
2029 1.1270e-01 -4.5915e-05 3.0937e-02 6.4103e-01 0.5215
2030 -2.8646e-02 -4.5915e-05 3.0937e-02 -1.6260e-01 0.8708
2031 -5.8154e-01 -7.8531e-03 5.2502e+00 -2.5037e-01 0.8023
2032 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2033 -4.1005e-01 -4.5915e-05 3.0937e-02 -2.3310e+00 0.0198
2034 2.1958e+00 -4.1691e-04 2.8081e-01 4.1445e+00 0.0000
2035 2.6590e+00 -8.6926e-04 5.8523e-01 3.4769e+00 0.0005
2036 1.7387e+00 -6.2255e-04 4.1923e-01 2.6863e+00 0.0072
2037 1.5198e+00 -3.9542e-04 2.6634e-01 2.9457e+00 0.0032
2038 3.6900e+00 -1.4860e-03 9.9980e-01 3.6919e+00 0.0002
2039 1.3576e+00 -2.1962e-04 1.4795e-01 3.5300e+00 0.0004
2040 1.1089e+00 -2.1101e-04 1.4216e-01 2.9417e+00 0.0033
2041 5.0391e-01 -1.1138e-04 7.5045e-02 1.8399e+00 0.0658
2042 -3.9613e-02 -4.5915e-05 3.0937e-02 -2.2495e-01 0.8220
2043 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2044 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2045 -1.5075e-01 -7.5473e-05 5.0852e-02 -6.6815e-01 0.5040
2046 -2.9173e-01 -4.5915e-05 3.0937e-02 -1.6583e+00 0.0973
2047 -5.2895e-02 -4.5915e-05 3.0937e-02 -3.0046e-01 0.7638
2048 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2049 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2050 -2.4993e-01 -4.5915e-05 3.0937e-02 -1.4207e+00 0.1554
2051 -4.0590e-01 -4.5915e-05 3.0937e-02 -2.3075e+00 0.0210
2052 4.3248e-02 -4.5915e-05 3.0937e-02 2.4614e-01 0.8056
2053 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2054 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2055 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2056 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2057 1.3586e-01 -4.5915e-05 3.0937e-02 7.7265e-01 0.4397
2058 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2059 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2060 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
2061 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
2062 -2.5286e-01 -8.5022e-05 5.7286e-02 -1.0561e+00 0.2909
2063 8.9167e-01 -5.8327e-04 3.9280e-01 1.4237e+00 0.1545
2064 -2.5018e-01 -4.5915e-05 3.0937e-02 -1.4221e+00 0.1550
2065 1.8582e-01 -4.5915e-05 3.0937e-02 1.0567e+00 0.2907
2066 -4.3137e-01 -4.5915e-05 3.0937e-02 -2.4522e+00 0.0142
2067 2.6198e+00 -5.0856e-04 3.4251e-01 4.4773e+00 0.0000
2068 -7.4393e-01 -4.5915e-05 3.0937e-02 -4.2292e+00 0.0000
2069 1.8077e+00 -3.9542e-04 2.6634e-01 3.5035e+00 0.0005
2070 3.0187e+00 -1.6012e-03 1.0772e+00 2.9101e+00 0.0036
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3916 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
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4034 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4035 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
4036 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
4037 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
4038 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
4039 1.8582e-01 -4.5915e-05 3.7134e-02 9.6451e-01 0.3348
4040 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
4041 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4042 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4043 1.8582e-01 -4.5915e-05 4.6429e-02 8.6257e-01 0.3884
4044 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4045 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4046 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4047 1.8582e-01 -4.5915e-05 6.1921e-02 7.4692e-01 0.4551
4048 1.8582e-01 -4.5915e-05 9.2904e-02 6.0978e-01 0.5420TH3.5.1 Mapping Local Moran’s I
jb_kulai.localMI <- cbind(jb_kulai_grid, localMI) %>%
rename(Pr.Ii = Pr.z....E.Ii..)
localMI_map <- tm_shape(jb_kulai.localMI) +
tm_fill(col = "Ii",
style = "pretty",
palette = "YlGn",
n = 7,
title = "local moran statistics") +
tm_borders(alpha = 0.5)
p_values <- tm_shape(jb_kulai.localMI) +
tm_fill(col = "Pr.Ii",
breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
palette="-RdBu",
title = "local Moran's I p-values") +
tm_borders(alpha = 0.5)
tmap_arrange(localMI_map, p_values, asp = 1, ncol = 2)
TH3.6 Hot and Cold Spot Analysis
The next local indicator of spatial autocorrelation to explore is hot and cold spot analysis with Gertis and Ord’s G-statistics, or \(G^*_i\) statistics.
# Compute distance weight matrix
jb_kulai_wgs <- jb_kulai_grid %>% st_transform(4326)
longitude <- map_dbl(jb_kulai_wgs$geometry, ~st_centroid(.x)[[1]])
latitude <- map_dbl(jb_kulai_wgs$geometry, ~st_centroid(.x)[[2]])
coords <- cbind(longitude, latitude)
# Compute adaptive distance weight matrix
knn <- knn2nb(knearneigh(coords, k = 8))
knn_lw <- nb2listw(knn, style = "B")
# Compute Gi* statistics
gi <- localG(jb_kulai_wgs$median_price, knn_lw)
jb_kulai.gi <- cbind(jb_kulai_wgs, as.matrix(gi)) %>% rename(gstat = as.matrix.gi.)gi_map <- tm_shape(jb_kulai.gi) +
tm_fill(
col = "gstat",
palette = "-RdBu",
title = "drug_use local Gi",
breaks = seq(from = -10, to = 10, by = 2)
) +
tm_borders(alpha = 0.5) +
tm_legend(position = c("RIGHT", "BOTTOM"))
tmap_arrange(medians_map, gi_map)Variable(s) "gstat" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
Variable(s) "gstat" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.